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Here's a link to a good question regarding Textbooks on Bayesian statistics from some time ago.

People suggested John Kruschke's "Doing Bayesian Data Analysis: A Tutorial Introduction with R and BUGS" as one of the best options to get an introduction to Bayesian statistics. Meanwhile, a potentially interesting book called "Bayesian and Frequentist Regression Methods" by Jon Wakefield was released, which also provides code for R and BUGS. Thus, they esentially both seem to cover the same topics.

Question 1: If you have read the book, would you recommend it to a frequentist economics masters graduate as both an introduction to Bayesian statstics and reference book for both frequentist and bayesian approaches?

Question 2: If you have read both Wakefield's and Kruschke's book, which one would you recommend better?

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I definitely do not like Kruschke's book. I read it, worked out a lot of examples, but didn't understand anything about bayesian inference! As an introductory book about bayesian statistics, you could better look at Scott Lynch, Introduction to Applied Bayesian Statistics and Estimation for Social Scientists, or at Tony Lancaster, An Introduction to Modern Bayesian Econometrics.

Wakefield's book is a good choice. But, how could I say?, he describes bayesian inference more than explaining it, because his point of view is a neutral one: "Each of the frequentist and Bayesian approaches have their merits and can often be used in tandem." I do not agree... But it's my own point of view :-) If you are going to read it, be prepared: the field is biostatistics (dental growth, prostate cancer, etc.) Moreover, you could be not interested in GEE (econometricians use GMM) or in nonparametric modeling. However, you can get a sense of Wakefield's book by looking at his courses. For example, http://courses.washington.edu/b571/lectures/

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    $\begingroup$ Odd. I found Kruschke's book very enlightening. In fact, I tried several other books, and kept returning to that one to figure out what the others were saying. $\endgroup$ – Matt May 5 '14 at 1:51
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RE: Q1, I took Wakefield's class, so I spent a lot of time with his book. It is clearly written and well-argued, and I recommend it highly as a reference. I am actually about to buy a copy right now -- that's how I found your question.

If you're particularly worried about learning Bayesian techniques as a frequentist, that's another good reason to try Wakefield's book. It puts into action a pragmatic view held by many at UW: that the choice of inferential method should be driven by the data analysis problem at hand. This doesn't prevent Wakefield and his colleagues from (rightly) marginalizing worthless branches of statistics such as fiducial inference, but compared to dogmatic Bayesian or frequentist viewpoints, it expands the repertoire of tools available to trainees and practitioners. If you haven't read the reviews by Larry Wasserman, Andrew Gelman, and Taeryon Choi, you can find them on Wakefield's site.

http://faculty.washington.edu/jonno/book/

I haven't read the other book, so I can't address Q2.

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